Explanation Given, The tessellation from Exercise 47 is given by, Case (i): When one vertex is occupied by a hexagon, the angle occupied one hexagon = 120 ∘ The remaining angle of 360 ∘ is = 360 ∘ − 120 ∘ = 240 ∘ Now four triangles can be occupied by the remaining 240 ∘ as such each triangle occupy 60 ∘ at its vertex. The tessellation with a combination of one hexagon and four triangles is not shown in the given figure. Case (ii): When one vertex is occupied by two hexagons, the angle occupied two hexagons = 120 ∘ + 120 ∘ = 240 ∘ The remaining angle of 360 ∘ is = 360 ∘ − 240 ∘ = 120 ∘ Now two triangles can be occupied by the remaining 120 ∘ as such each triangle occupy 60 ∘ at its vertex. Thus, a tessellation with a combination of two hexagon and two triangles is possible. Case (iii): When one vertex is occupied by three hexagons, the angle occupied three hexagons = 120 ∘ + 120 ∘ + 120 ∘ = 360 ∘ Now no more triangle can be occupied by the vertex. The tessellation with a combination of three hexagons is not shown in the figure. The number of possible hexagon-triangle combinations possible at the vertex of a tessellation. Number of hexagon at a vertex Amount of angle used by the hexagon of total 360 ° at the vertex Amount of angle remaining for the triangle Does 60 ° divide this number To determine b) To find: The series of numbers representing the given tessellation. To determine c) To find: The series of numbers representing the given tessellation. To determine d) To find: The series of numbers representing the given tessellation.

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ISBN: 9780135902783

Author: Pirnot

Publisher: PEARSON

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Chapter 9.6, Problem 51E

To determine

a)

To find:

The series of numbers representing the given tessellation.

To determine

b)

To find:

The series of numbers representing the given tessellation.

To determine

c)

To find:

The series of numbers representing the given tessellation.

To determine

d)

To find:

The series of numbers representing the given tessellation.

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Chapter 9.6, Problem 50E

Chapter 9.6, Problem 52E

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a) To find: The series of numbers representing the given tessellation.

Solution Summary: The author explains the tessellation from Exercise 47. When one vertex is occupied by a hexagon, the angle of one hexagon is =120circ .

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a) To find: The series of numbers representing the given tessellation.

b) To find: The series of numbers representing the given tessellation.

c) To find: The series of numbers representing the given tessellation.

d) To find: The series of numbers representing the given tessellation.

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Chapter 9 Solutions

a)

To find:

The series of numbers representing the given tessellation.

b)

To find:

The series of numbers representing the given tessellation.

c)

To find:

The series of numbers representing the given tessellation.

d)

To find:

The series of numbers representing the given tessellation.